Mathematical Education: Modularisation vs Linear Syllabus

A levels are a crucial way that universities select candidates for their courses, so it is important that these qualifications meet the needs of higher education institutions. To ensure that they support progression to further education, higher education or employment, we are working with Ofqual, the awarding organisations and higher education institutions to ensure universities and learned bodies can be fully involved in their development. We specifically want to explore where linear A levels can be adapted to provide the depth of synoptic learning which the best universities value. [4.47]

I fully support the LMS Response to the Education White Paper which says, in particular:

Mathematics assessment strongly benefits from end-of-course, linear assessment, and we support moves towards this both at GCSE and at A-level. Effective mathematics teaching is a long-term project, whose goals are undermined by a modular structure: mathematics is a body of unifying ideas which often take time to assimilate.

But, to avoid any ambiguity, I have to emphasise that the present post is written by me in my private capacity and does not necessarily reflect views of the LMS or any other institution or organisation.

I believe that demodularisation of school mathematics will be welcomed by the universities, but with one important caveat: demodularisation should be introduced step-by-step as evolution, not revolution, to avoid damaging shocks of the kind that happened in 2002 with previous reform, when scared students became reluctant to take Mathematics A Levels.

As an admission tutor from an elite university wrote to me,

Maths A-levels are not perfect — we all know that. n particular, the modular scheme (no synoptic paper) [… ] is damaging. However retaining the current scheme, perhaps with some tweaks, will be far less damaging than trying to overhaul the system.

My personal opinion is that demodularisation is worth trying. I suggest it can be achieved by means of a low-cost evolution by

shaping linear syllabus,

gradual introduction of synoptic questions into exam papers, and

step-by-step retraining of teachers over several years.

But this is difficult, and requires a carefully coordinated work of a number of bodies over many years. In my opinion, it is best do nothing than rush unprepared decisions.

Responses

Here is a report about a new study on teenage brains. Apparently not only (as already known) in very early childhood, but until adulthood too, “unused” brain circuits are ruthelessly deleted in the browing brain. This strenghtens the need for advanced, complex input in teenagers’ brains and not as late at the university.

My impression from tutoring students is that there is a gap in the current education system (at least here in Germany), because despite growing amounts of facts etc. they have to learn, during the last years in school and within the first years in the university, the real intellectual level declines. Often students complain that the contents in first few semesters at university were boring and below school level.

… and it explains this this observation by Dennis Sullivan:
“There’s an interesting theory that, among mathematicians for example, a person may discover they like mathematics and have a strong aptitude. They get so involved in it that their personality development is arrested at that point. They just stop caring about the finer points of their finishing, you might say. I’ve seen this in
every one of my six children. They’re like little mathematicians or little scientists, then for some reason that usually washes out. They get interested in other things. For some of us, like me, it didn’t wash out.”

I am wondering what your thoughts are on linear and semstered learning in highschool. I think especially in the lower grades (8&9), that learning math in a linear system would prove beneficial. I am a tutor, and find that any student is capable of doing math if they practice and repeat concepts enough times. Working within a linear systems would allow more time to practice concepts ans solidify skills needed to progress…I think